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If a company spends r million dollars on research, it sales will be s million dollars, where r and s are related by s² = -55. (a) Find ds/dr by implicit differentiation and evaluate it at r=4, s= 3. [Hint: Differentiate the equation with respect to r.] (b) Find dr/ds by implicit differentiation and evaluate it at r=4,s3. [Hint: Differentiate the original equation with respect to s.] (c) Interpret your answer to part (a) as a rate of change. O Changing research will not affect sales. O Given ds/dr = n. this means that the rate of change of sales with respect to research expenditures is n, so that increasing research by one million dollars increase sales by about n million dollars (at these levels of r and s). O Given ds/dr = n, this means that the rate of change of research expenditures with respect to sales is n, so that increasing sales by one million dollars will increase research by about n million dollars (at these levels of r and s). Interpret your answer to part (b) as a rate of change. O Given drids = m, this means that the rate of change of sales with respect to research expenditures is n. so that increasing research by one million dollars will increase sales by about m million dollars (at these levels of rand s). Given dr/ds=m, this means that the rate of change of research expenditures with respect to sales is m, so that increasing sales by one million dollars wi increase research by about m million dollars (at these levels of rand s). Changing sales will not affect research

If a company spends r million dollars on research, it sales will be s million dollars, where r and s are related by s² = -55. (a) Find ds/dr by implicit differentiation and evaluate it at r=4, s= 3. [Hint: Differentiate the equation with respect to r.] (b) Find dr/ds by implicit differentiation and evaluate it at r=4,s3. [Hint: Differentiate the original equation with respect to s.] (c) Interpret your answer to part (a) as a rate of change. O Changing research will not affect sales. O Given ds/dr = n. this means that the rate of change of sales with respect to research expenditures is n, so that increasing research by one million dollars increase sales by about n million dollars (at these levels of r and s). O Given ds/dr = n, this means that the rate of change of research expenditures with respect to sales is n, so that increasing sales by one million dollars will increase research by about n million dollars (at these levels of r and s). Interpret your answer to part (b) as a rate of change. O Given drids = m, this means that the rate of change of sales with respect to research expenditures is n. so that increasing research by one million dollars will increase sales by about m million dollars (at these levels of rand s). Given dr/ds=m, this means that the rate of change of research expenditures with respect to sales is m, so that increasing sales by one million dollars wi increase research by about m million dollars (at these levels of rand s). Changing sales will not affect research

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.CR: Chapter 3 Review
Problem 8CR
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If a company spends r million dollars on research, it sales will be s million dollars, where r and s are related by s² = ³-55. (a) Find ds/dr by implicit differentiation and evaluate it at r = 4, s = 3. [Hint: Differentiate the equation with respect to r.] (b) Find dr/ds by implicit differentiation and evaluate it at r= 4, s= 3. [Hint: Differentiate the original equation with respect to s.] 호 dr ds (c) Interpret your answer to part (a) as a rate of change. O Changing research will not affect sales. Given ds/dr = n, this means that the rate of change of sales with respect to research expenditures is n, so that increasing research by one million dollars wi increase sales by about n million dollars (at these levels of r and s). Given ds/dr = n, this means that the rate of change of research expenditures with respect to sales is n, so that increasing sales by one million dollars will increase research by about n million dollars (at these levels of r and s). Interpret your answer to part (b) as a rate of change. O Given dr/ds = m, this means that the rate of change of sales with respect to research expenditures is n, so that increasing research by one million dollars will increase sales by about m million dollars (at these levels of r and s). Given dr/ds = m, this means that the rate of change of research expenditures with respect to sales is m, so that increasing sales by one million dollars will increase research by about m million dollars (at these levels of r and s). O Changing sales will not affect research.
Transcribed Image Text:If a company spends r million dollars on research, it sales will be s million dollars, where r and s are related by s² = ³-55. (a) Find ds/dr by implicit differentiation and evaluate it at r = 4, s = 3. [Hint: Differentiate the equation with respect to r.] (b) Find dr/ds by implicit differentiation and evaluate it at r= 4, s= 3. [Hint: Differentiate the original equation with respect to s.] 호 dr ds (c) Interpret your answer to part (a) as a rate of change. O Changing research will not affect sales. Given ds/dr = n, this means that the rate of change of sales with respect to research expenditures is n, so that increasing research by one million dollars wi increase sales by about n million dollars (at these levels of r and s). Given ds/dr = n, this means that the rate of change of research expenditures with respect to sales is n, so that increasing sales by one million dollars will increase research by about n million dollars (at these levels of r and s). Interpret your answer to part (b) as a rate of change. O Given dr/ds = m, this means that the rate of change of sales with respect to research expenditures is n, so that increasing research by one million dollars will increase sales by about m million dollars (at these levels of r and s). Given dr/ds = m, this means that the rate of change of research expenditures with respect to sales is m, so that increasing sales by one million dollars will increase research by about m million dollars (at these levels of r and s). O Changing sales will not affect research.
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